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What is the Square Root of 409?

The square root of 409 is 20.2237484162. Calculate another value or review the exact form, nearby perfect powers, and verification.

Answer

Square Root√409 = 20.2237484162
CalculatedNon-perfect squareIrrational
Exact form√409
Perfect squareNo
Number typeIrrational
Verification20.22374841622 ≈ 409

On this page

How the answer is calculated

We solve x2 = 409. The resulting value is x = 20.2237484162.

Verification: 20.22374841622 ≈ 409.

Simplified radical form

The square root of 409 in simplified radical form is √409.

There are no square factors that can be taken outside the radical, so √409 is already in simplest radical form.

Nearest Perfect squares

PositionBaseValue
Lower or equal20400
Upper or equal21441

Nearby square roots

NumberSquare root
√40620.1494416796
√40720.1742410018
√40820.1990098767
√40920.2237484162
√41020.2484567313
√41120.2731349327
√41220.2977831302

Number properties

Is 409 a perfect square?

No. Its square root is not a whole number.

Is the square root rational or irrational?

√409 is irrational because 409 is not a perfect square.

Visual guide

Square Root function graph

See how the result changes as the input moves across positive and negative values. Square roots are shown for non-negative inputs; cube roots continue through negative inputs.

Common questions

Frequently asked questions

It asks for the number that, when raised to the power of 2, equals 409.